Kuramoto-Sivashinsky方程的高精度差分格式  

High-order difference scheme for the Kuramoto-Sivashinsky equation

作　　者：付瑶 王晓峰 刘佳垚 付天浩 FU Yao;WANG Xiaofeng;LIU Jiayao;FU Tianhao(School of mathematics and statistics,Minnan Normal University,Zhangzhou,Fujian 363000,China)

机构地区：[1]闽南师范大学数学与统计学院,福建漳州363000

出　　处：《闽南师范大学学报（自然科学版）》2023年第3期83-89,共7页Journal of Minnan Normal University：Natural Science

基　　金：福建省自然科学基金(2020J01796)。

摘　　要：对周期边界Kuramoto-Sivashinsky方程建立了一个四阶精度差分格式.该格式在时间上是三层的,并且是线性的,同时该格式是质量守恒和能量耗散的.通过离散能量法证明了该格式解的唯一性,有界性和收敛性.数值实验验证了理论分析的正确性,在时间和空间上分别达到二阶精度和四阶精度.A fourth-order precision difference scheme is established for the Kuramoto-Sivashinsky equation with periodic boundary.The scheme is three-layer and linear in time.Meanwhile,the scheme is mass conservative and energy dissipative.The uniqueness,boundedness and convergence of the solution of the scheme are proved by the discrete energy method.The numerical experiments verify the correctness of the theoretical analysis,and reach the second and fourth order accuracy in time and space respectively.

关 键 词：KURAMOTO-SIVASHINSKY方程 差分格式 守恒性 收敛性 

分 类 号：O241.82[理学—计算数学]